Class:
Name:
(
) Date:
Experiment 2e
2e Equivalent resistance of resistors in
parallel
Objective
To find out how the equivalent resistance of resistors connected in
parallel is related to the individual resistances of them.
Background information
1
or
2
The resistance of a conductor is defined as:
voltage across conductor
Resistance =
current through conductor
R=
V
I
By measuring the current I through a conductor when a known
voltage V is applied across it, the resistance of the conductor
V
can be determined from the formula R = .
I
Apparatus
❏ several carbon resistors of different resistance (including two 20-Ω resistors)
❏ 1 voltmeter
❏ 1 ammeter
❏ 1 battery box
❏ 1 switch
❏ several connecting leads
New Physics at Work (Second Edition)
© Oxford University Press 2007
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Experiment 2e
Class:
Name:
) Date:
Procedure
✐ The resistance of
a carbon resistor is
indicated by the colour
of the rings. Visit the
website http://www.
csgnetwork.com/
resistcolcalc.html to find
out how to calculate
the resistance from the
colour codes.
(
1
Set up the apparatus as shown in Figure 2e-1:
(a)Connect two 20-Ω resistors (R1 and R2) in parallel, and in series
with an ammeter, a 3-V battery box and a switch.
(b) Connect a voltmeter across the two resistors.
✐ Carbon resistors of
10 Ω and 100 Ω can be
found in Westminster
electromagnetic kit.
battery box
✐ The e.m.f. of
the battery and the
resistances of the
resistors can be changed
to other values available.
ammeter
switch
voltmeter
20-8 resistor
20-8 resistor
A
R1 = 20 8
R2 = 20 8
V
Fig 2e-1
2
(a) Measure the current I of the circuit using the ammeter and the
voltage V across the two resistors using the voltmeter.
(b)Record the results in Table 2e-1 on p.35 and calculate the
V
equivalent resistance Req of the two resistors from .
I
34
New Physics at Work (Second Edition)
© Oxford University Press 2007
Class:
Name:
(
Experiment 2e
) Date:
3
Repeat with other combinations of V, R1 and R2. Record the results in
Table 2e-1 and calculate the equivalent resistance Req.
✎
Results:
Equivalent
resistance
Resistance of
resistor R1 / Ω
Resistance of
resistor R2 / Ω
Voltage across
two resistors
V/V
Current of
circuit I / A
20
20
2.6
0.25
10.4
20
100
2.7
0.16
16.9
20
200
2.7
0.15
18.0
30
100
2.7
0.12
22.5
100
100
2.8
0.06
46.7
(Req =
V
)/Ω
I
Table 2e-1
4
Calculate the values of
Table 2e-2.
✎
1 1
1
,
and
. Record the results in
R1 R2
Req
Results:
1
/ Ω–1
R1
1
–1
R2 / Ω
1
/ Ω–1
Req
0.05
0.05
0.096
0.05
0.01
0.059
0.05
0.005
0.056
0.033
0.01
0.044
0.01
0.01
0.021
Table 2e-2
Discussion
Hint
Consider the reciprocals
of Req, R1 and R2.
✎
How is the equivalent resistance Req of the two resistors related to the
individual resistances R1 and R2 of them?
After allowing for errors,
New Physics at Work (Second Edition)
1
1
1
is equal to
+
.
Req
R1
R2
© Oxford University Press 2007
35
Experiment 2e
Class:
Name:
(
) Date:
The reciprocal of equivalent resistance of resistors connected in
sum
parallel is equal to the ________________________
of the reciprocals
of individual resistances of them.
Further thinking
✎
By considering the current and voltage of each of the two resistors
connected in parallel, derive the relationship between the equivalent
resistance Req and the individual resistances R1 and R2 of them
mathematically. What will be the relationship if more resistors are
connected in parallel?
As the voltage across each resistor is the same,
V
R1
V
current flowing through R2: I2 =
R2
current flowing through R1: I1 =
total current flowing from the battery: I =
V
Req
Since the current flowing from the battery is equal to the sum of currents through
each resistor:
I = I1 + I2
V
V
V
=
+
Req
R1
R2
1
1
1
⇒
=
+
Req
R1
R2
⇒
If more resistors are connected in series, the reciprocal of equivalent resistance will
still be equal to the sum of the reciprocals of individual resistances of them.
36
New Physics at Work (Second Edition)
© Oxford University Press 2007